Related papers: Multivariate Group Entropies, Super-exponentially …
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for…
Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…
In this expository paper we describe an unifying approach for many known entropies in Mathematics. First we recall the notion of semigroup entropy h_S in the category S of normed semigroups and contractive homomorphisms, recalling also its…
We present a general definition of entropy in the setting of pre-ordered semigroups, extending the notion of topological entropy. From our definition, we obtain the basic properties exhibited by various entropy-like theories encountered in…
One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…
For certain groups, parabolic subgroups appear as stabilizers of flags of sets or vector spaces. Quotients by these parabolic subgroups represent orbits of flags, and their cardinalities asymptotically reveal entropies (as rates of…
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…
Algebraically, entropy can be defined for abelian groups and their endomorphisms, and was latter extended to consider objects in a Flow category derived from abelian categories, such as $R\textit{-}Mod$ with $R$ a ring. Preradicals are…
We shall prove that the celebrated R\'enyi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the $Z$-entropies. Each of them, under suitable hypotheses, generalizes the celebrated…
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…
We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion…
A new combinatorial-probabilistic diagnostic entropy has been introduced. It describes the pair-wise sum of probabilities of system conditions that have to be distinguished during the diagnosing process. The proposed measure describes the…
The description of the dynamics of complex systems, in particular the capture of the interaction structure and causal relationships between elements of the system, is one of the central questions of interdisciplinary research. While the…